The following disclosure relates to electrical circuits and signal processing.
Aligning the phases of two or more signals in a communications system can be useful. The signals can be information signals at multiple points in a signal path. For example, in a communications system that uses feedback, the phase of a feedback signal may need to be aligned with the phase of a forward path signal for the system to operate correctly or efficiently.
A complex signal (represented, for example, by an in-phase component and a quadrature component) can be used to transmit information using symbols that are specific combinations of the components of the complex signal. For example, an in-phase (I) and quadrature (Q) representation of a complex signal can have four symbols, corresponding to the following combinations of the amplitudes of (I,Q): (1,1); (1,−1); (−1,1); and (−1,−1). FIG. 1A shows a plot 100 of the in-phase and quadrature components of two complex signals. Two constellations of symbols, each constellation corresponding to a complex signal, are shown. Each of the constellations includes four symbols that represent the symbols that can be transmitted by the corresponding complex signal. One constellation is represented by four circles (e.g., circle 110), and the other constellation is represented by four crosses (e.g., cross 120). The constellation represented by the crosses is rotated relative to the constellation represented by the circles by an angle of φ, indicating that the corresponding complex signals are rotated relative to each other.
A relative rotation between two complex signal constellations can have several causes. In a typical scenario, a first (I,Q) signal pair is used to modulate a radio-frequency (RF) carrier. The modulated carrier, an RF signal, undergoes analog processing steps, after which the modulated carrier is demodulated. A second (I,Q) signal pair results from the demodulation. Any difference in phase between the modulated carrier before the processing steps and the modulated carrier after the processing steps is manifested as a relative rotation between the baseband constellations corresponding to the first and second (I,Q) signal pairs.
FIG. 1B shows a plot 105 of the in-phase and quadrature components of the two complex signals from FIG. 1A where the phase of the complex signal with the constellation represented by the crosses (e.g., cross 120) has been rotated by −φ to align the two constellations and therefore align the two complex signals. Aligning two complex signals is equivalent to making the relative rotation between the signals substantially zero.
An example of a component in a communications system that uses feedback is a Cartesian feedback transmitter. In a Cartesian feedback transmitter, a complex feedback signal is subtracted from a complex input signal to produce a complex error signal. The complex error signal is amplified and filtered to produce an intermediate signal, which is then modulated for transmission. The modulated signal is also demodulated in the transmitter to produce the complex feedback signal. Using Cartesian feedback in a transmitter improves the linearity of the transmitter, but properly aligning the phases of the complex intermediate signal and the complex feedback signal is important.
The complex feedback signal typically has a different phase than the complex intermediate signal because of, for example, delays in the RF signal path or a phase difference between the oscillator signal used during modulation and the oscillator signal used during demodulation. A change in output power level or a change in carrier frequency can also cause a relative rotation between the complex intermediate signal and the complex feedback signal. The phase of the complex intermediate signal can be adjusted (e.g., by using a rotator circuit) to align the complex intermediate signal and the feedback signal. The adjustment of the phase of the complex intermediate signal can be controlled based on, for example, an estimate of the relative rotation between the complex intermediate signal and the complex feedback signal.
One technique that can be used to estimate the phase difference between the complex intermediate signal and the complex feedback signal is to multiply the in-phase component of the intermediate signal (IIN) by the quadrature component of the feedback signal (QFB) and to multiply the quadrature component of the intermediate signal (QIN) by the in-phase component of the feedback signal (IFB), all multiplication being done in the analog domain. The second product (QIN IFB) is then subtracted from the first product (IIN QFB), and the result is integrated. A rotator circuit uses the integrated result to rotate the phase of the intermediate signal with respect to the feedback signal.
In practice, use of the IIN QFB−QIN IFB phase alignment technique described above may require analog multipliers capable of handling signals that have a very large dynamic range. The analog multipliers can be difficult to design, and may require an unacceptable amount of power and/or complexity to implement.